Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
1 kgk

A 1 kg mass on a spring makes 30 complete oscillations in 24 s. Find the frequency f of the oscillation.

m = 1 kgN = 30t = 24 s
f = Hz
2.Easy
3.1 kgk = 50 N/m

A 3.1 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.1 kgk = 50 N/m
f = Hz
3.Medium
L = 1.7 m

A simple pendulum has a length of 1.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.7 mg = 9.81 m/s²
T = s
4.Medium
0.4 kgk = 200 N/mA = 12 cmx = 4 cm

A 0.4 kg mass on a spring with k = 200 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 4 cm from equilibrium.

m = 0.4 kgk = 200 N/mA = 12 cmx = 4 cm
v = m/s
5.Hard
0.5 kgk = 2000 N/m350 m/s

A 5 g bullet moving at 350 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 2000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 5 gv = 350 m/sM = 0.5 kgk = 2000 N/m
A = cm
6.Hard
t (s)x (cm)t = ?4.2

A body oscillates in simple harmonic motion with period 3.1 s and amplitude 6 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.2 cm?

T = 3.1 sA = 6 cmx = 4.2 cm
t = s

Answer key

  1. 1. f = 1.25 Hz
  2. 2. f = 0.6392 Hz
  3. 3. T = 2.616 s
  4. 4. v = 2.53 m/s
  5. 5. A = 5.507 cm
  6. 6. t = 0.3826 s

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